Some devices are intended to be subject to high amounts of thermal power, which can cause thermal deformation and other associated problems that can limit sensitivity in a general sense. For example, the Ad-LIGO [see reference 1, incorporated herein by reference in its entirety] and Advanced Virgo [see reference 2 incorporated herein by reference in its entirety] main Fabry Perot minors are intended to be subject to nearly 1 MW of standing laser light over a Gaussian spot size of ˜6 cm radius.
The current limit for high reflectivity coatings is absorption of roughly 0.25 ppm of the reflected beam. An absorption level around 0.3-0.4 ppm is routinely obtained on high reflectivity minors by use of Ti doped Ta2O5 [see reference 3, incorporated herein by reference in its entirety]. The advanced interferometers' design specifications call for a target of 0.5 ppm absorption, and a maximum of 1 ppm [see references 4, 5 incorporated herein by reference in their entirety]. Thus, the mirrors will be subject to 0.25 to 1 W of heating with a power distribution that matches that of the stored beam.
Such heating would produce a minor deformation (thermal lensing) that would impede the full performance of the interferometer [see references 6-8 incorporated herein by reference in their entirety]. This effect is particularly damaging to the mode profile matching of the main beam stored in the main, 3 or 4 km Fabry Perot cavities to the RF modulated sidebands stored in the short section of the Michelson interferometer, which are used to control the interferometer [see reference 9, incorporated herein by reference in its entirety]. This problem can occur at lower power, due to the higher absorption of older designs minors [see references 10-13 incorporated herein by reference in their entirety].
To mitigate this problem a Thermal Compensation System (TCS), which shapes an annular CO2 laser beam and projects such beam on the mirror periphery, has been implemented in the present LIGO and Virgo. The CO2 beam is absorbed within microns by the silica on the surface of the mirror and produces a thermal deformation balancing that which has been produced by the stored laser beam heat.
This relatively simple solution is not acceptable in the advanced detectors due to the difficulties in stabilizing a CO2 laser intensity. The thermo-elastic noise and the radiation pressure fluctuations imposed on the test masses from the TCS would overwhelm the Gravitational Wave (GW) signal.
A solution to avoid disturbing the very sensitive main Fabry Perot minors is to implement, behind the inner test masses, a hot ring and a Compensation Plate (CP) acted on by a CO2 laser [see references 14, 15 incorporated herein by reference in their entirety]. The hot ring annular heating technique has been tested directly on the test masses to modify the radius of curvature of a test mass in the GEO interferometer [see reference 16, incorporated herein by reference in its entirety]. An Ohmic heating ring was placed within few mm from the minor surface.
The hot ring technique will be applied in Advanced LIGO for thermal lensing corrections. In Advanced LIGO the radial escape from the CP of the applied heat limits the correction effectiveness, thus gold plating will be applied to the CP barrel surface to depress its radial black body radiation. The negative thermal lensing thus applied on the CP will sufficiently compensate for the deformation of the main mirrors.
However, the above solutions are less than ideal because they are directed at mitigating with a counter deformation the negative effects of a deformation on the mirror.